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We show that the # 0 2 high e-degrees coincide with the high edegrees. We also show that not every properly # 0 2 e-degree is high. 1 Introduction Enumeration reducibility is the notion of relative enumerability of sets: a set A is enumeration reducible (or simply e-reducible) to a set B, in symbols, A # e B, if there is an e#ective procedure for enumerating A given any enumeration of B. Formally, we define A # e B if there is some computably enumerable set # (called in this context an enumeration operator or simply an e-operator) such that A = {x : (# finite D)[#x, D# # #&D # B]} (throughout the paper we identify finite sets with their canonical indices). We denote by # e the equivalence relation generated by the preordering relation # e and deg e (A) denotes the equivalence class (or the e-degree) of A. The partially ordered structure of the e-degrees is denoted by D e ; its partial ordering is denoted by #. D e is, in fact, an upper semilattice with least el...